F. Combes (1,2,3), S. Retout (2, 3), N. Frey (2) and F. Mentré (1)
(1) INSERM, UMR 738, Univ Paris Diderot, Sorbonne Paris cité, Paris, France; (2) Pharma Research and Early Development, Clinical Pharmacology, F. Hoffmann-La Roche ltd, Basel, Switzerland; (3) Institut Roche de Recherche et Médecine Translationnelle, Boulogne-Billancourt, France
Objectives: In 2009, Savic et al [1] showed that high shrinkage caused by poorly informative study designs can hide or induce correlation between estimated individual parameters (EBE) and covariates. That work did not explore the impact on the power of tests used for covariate detection. The present work investigates the impact of various designs, along with the associated shrinkages, on the power to detect the effect of a continuous covariate of i) the correlation test (CT) based on EBEs, ii) the likelihood ratio test (LRT).
Methods: A one compartment pharmacokinetic (PK) model with oral first-order absorption and a weight (WT) effect on volume (coded with a power function) was used for simulation. To obtain various level of shrinkage, different values of random effect variability (20 and 50%), of proportional residual error (30 and 40%), of β (0, 0.2, 0.5 and 1), as well as different number of PK samples per subject (2, 3 or 5), were combined. Each combination was simulated 1000 times with 500 subjects. Predicted shrinkage was computed using the approximation of the Bayesian information Matrix [2-3]. NONMEM 7.2 [4] with algorithms FOCEI and SAEM (followed by IMP for likelihood computation) was used to perform parameter estimation [5]. The type 1 error and the power of LRT and CT (from EBEs after each estimation) were computed as well as the observed shrinkage.
Results: The observed shrinkages were similar with both algorithms and were in agreement with the predicted shrinkages. As expected, the power of LRT and CT for detecting the WT effect decreased with the informativeness of the study design and its associated shrinkage. However, two unexpected outcomes were found: 1) analysis of the EBEs by CT had the same power as the LRT even in case of a sparse PK sampling and high shrinkage; 2) population parameters estimated by SAEM were less biased and less spread than with FOCEI even in case of a rich PK sampling.
Conclusion: As expected, informativeness of study design influenced the power of tests used for covariate detection. CT based on EBEs, even with a sparse PK sampling, was as powerful as LRT to detect covariate influence. These results need to be confirmed by varying model complexity, covariate effects and design. SAEM was a more accurate and precise algorithm than FOCEI to estimate population parameter even with rich PK sampling and a simple model.
References:
[1] Savic RM, Karlsson MO. Importance of shrinkage in empirical bayes estimates for diagnostics: problems and solutions. AAPS J. 2009 Sep;11(3):558-69
[2] Combes F, Retout S, Frey N, Mentré F. Prediction of shrinkage of individual parameters using the Bayesian information matrix in nonlinear mixed-effect models with application in pharmacokinetics. PAGE (Population Approach Group in Europe) 2012; Abstr 2442, [www.page-meeting.org/?abstract=2442]
[3] Merlé Y, Mentré F. Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model. J Pharmacokinet Biopharm. 1995 Feb;23(1):101-25
[4] Beal S, Sheiner LB, Boeckmann A and Bauer RJ. NONMEM User’s guides. (1989-2009), Icon development Solutions, Ellicott City, USA 2009
[5] Gibianski L, Gibianski E and Bauer R. Comparison of Nonmem 7.2 estimation methods and parallel processiong efficiency on a target-mediated drug disposition model. J pharmacokinet pharmacodyn 2012 Feb;39(1):17-35
Reference: PAGE 22 (2013) Abstr 2829 [www.page-meeting.org/?abstract=2829]
Poster: Study Design